References
- W.M. Abd-Elhameed, E.H. Doha, and Y.H. Youssri, New wavelets collocation method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds, Abstr. Appl. Anal. (2013). Article ID 542839.
- S. Alkan and V.F. Hatipoglu, Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order, Tbilisi Math. J. (2017), pp. 10.
- A. Arikoglu and I. Ozkol, Solution of fractional differential equations by using differential transform methods, Chaos Soliton Fract. 34(5) (2007), pp. 1473–1481. doi: 10.1016/j.chaos.2006.09.004
- M. Bahmanpour and M.A.F. Araghi, A method for solving fredholm integral equations of the first kind based on chebyshev wavelets, Anal. Theory Appl. 29 (2013), pp. 197–207.
- J. Biazar and H. Ebrahimi, Chebyshev wavelets approach for nonlinear systems of Volterra integral equations, Comput. Math. Appl. 63(3) (2012), pp. 608–616. doi: 10.1016/j.camwa.2011.09.059
- A.A. El-Sayed, Numerical approach for solving space fractional order diffusion equations using shifted Chebyshev polynomials of the fourth kind, Turk. J. Math. 40 (2016), pp. 1283–1297. doi: 10.3906/mat-1503-20
- M.H. Heydari, M.R. Hooshmandasl, F. Mohammadi, and C. Cattani, Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations, Commun. Nonliear. Sci. 19(1) (2014), pp. 37–48. doi: 10.1016/j.cnsns.2013.04.026
- A.M. Houria and B. Omar, Simulation study of nonlinear reverse osmosis desalination system using third and fourth Chebyshev wavelet methods, Match Commun. Math. Comput. Chem. 75(3) (2016), pp. 629–652.
- R.L. Jian, P. Chang, and A. Isah, New operational matrix via Genocchi polynomials for solving Fredholm-Volterra fractional integro-differential equations, Adv. Math. Phys. 2017 (2017), pp. 1–12.
- Z. Meng, L. Wang, H. Li, and Z. Wei, Legendre wavelets method for solving fractional integro-differential equations, Int. J. Comput. Math. 92(6) (2015), pp. 1275–1291. doi: 10.1080/00207160.2014.932909
- F. Mirzaee and S.F. Hoseini, Application of Fibonacci collocation method for solving Volterra-Fredholm integral equations, Appl. Math. Comput. 273 (2016), pp. 637–644.
- S.T. Mohyud-Din, H. Khan, M. Arif, and M. Rafiq, Chebyshev wavelet method to nonlinear fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions, Adv. Mech. Eng. 9(3) (2017), pp. 1–8. doi: 10.1177/1687814017694802
- S. Momani and M.A. Noor, Numerical methods for fourth-order fractional integro-differential equations, Appl. Math. Comput. 182(1) (2006), pp. 754–760.
- Y. Nawaz, Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations, Comput. Math. Appl. 61(8) (2011), pp. 2330–2341. doi: 10.1016/j.camwa.2010.10.004
- D. Nazari Susahab and M. Jahanshahi, Numerical solution of nonlinear fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions, Int. J. Industrial Mathematics 7 (2015), pp. 63–69.
- I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Academic Press, New York, 1999.
- H. Saeedi, M.M. Moghadam, N. Mollahasani, and G.N. Chuev, A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order, Commun. Nonlinear. Sci. 16(3) (2011), pp. 1154–1163. doi: 10.1016/j.cnsns.2010.05.036
- P.K. Sahu and S.S. Ray, A numerical approach for solving nonlinear fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions, Int. J. Wavelets Multi. 14(5) (2016).
- S. Islam, I. Aziz, and M. Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, Int. J. Comput. Math. 90(9) (2013), pp. 1971–1989. doi: 10.1080/00207160.2013.770481
- N.H. Sweilam, A.M. Nagy, I.K. Youssef, and M.M. Mokhtar, New spectral second kind Chebyshev wavelets scheme for solving systems of integro-differential equations, Int. J. Appl. Comput. Math. 3(2) (2017), pp. 333–345. doi: 10.1007/s40819-016-0157-8
- Y. Wang and Q. Fan, The second kind Chebyshev wavelet method for solving fractional differential equations, Appl. Math. Comput. 218 (2012), pp. 8592–8601.
- Y. Wang and L. Zhu, Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Adv. Differ. Equ-Ny. 2017(1) (2017), pp. 27. doi: 10.1186/s13662-017-1085-6
- S. Yuzbasi, Numerical solutions of system of linear Fredholm-Volterra integro-differential equations by the Bessel collocation method and error estimation, Appl. Math. Comput. 250(21) (2015), pp. 320–338.
- S. Yuzbasi, A collocation method based on Bernstein polynomials to solve nonlinear Fredholm-Volterra integro-differential equations, Appl. Math. Comput. 273 (2016), pp. 142–154.
- X. Zhang, B. Tang, and Y. He, Homotopy analysis method for higher-order fractional integro-differential equations, Comput. Math. Appl. 62(8) (2011), pp. 3194–3203. doi: 10.1016/j.camwa.2011.08.032
- F. Zhou and X. Xu, The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients, Appl. Math. Comput. 280 (2016), pp. 11–29.
- L. Zhu and Q. Fan, Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW, Commun. Nonliear. Sci. 18 (2013), pp. 1203–1213. doi: 10.1016/j.cnsns.2012.09.024